Wavelets in Statistics: Discussion
نویسنده
چکیده
We congratulate the three authors for their thought-provoking and original work. We thank Guy Nason for the invitation to discuss the papers presented in this stimulating session. Lee and McCoy propose new wavelet shrinkage function estimators. We discuss various wavelet shrinkage estimators, including those of Lee and McCoy, in the context of penalty functions. The paper by von Sachs concerns nonstationary processes and overcomplete systems. We make some comments concerning di erent types of overcomplete systems.
منابع مشابه
Wavelet analysis and its statistical applications
In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where it is reasonable to consider such methods to be another standard tool of the applied statistician rather than a research novelty. With that in mind, this paper gives a relatively accessible introduction to standard wavelet analysis and provides a revi...
متن کاملComments on « Wavelets in Statistics : a Review » by a . Antoniadis
I would like to congratulate Professor Antoniadis for successfully outlining the current state-of-art of wavelet applications in statistics. Since wavelet techniques were introduced to statistics in the early 90's, the applications of wavelet techniques have mushroomed. There is a vast forest of wavelet theory and techniques in statistics and one can find himself easily lost in the jungle. The ...
متن کاملRanklets: A Qualitative Review
This paper reviews Ranklets, a family of multiscale, orientation-selective , non-parametric features modeled on Haar wavelets. Ranklets are related to wavelets and rank statistics. At the inception, a basic discussion on Ranklets is presented here. Next a focus is given to the various algorithms used so far to compute Ranklets with their complexities. The different applications of Ranklets in t...
متن کاملWavelets and Natural Image Statistics
It is well-known that wavelets provide a transformation of image data that has excellent properties with respect to image compression. The reasons for the compression ability of wavelets however have not been fully understood. In this paper we show that there is an interesting connection between wavelets and statistical properties of real-world images. This might lead to new theoretical and pra...
متن کاملWavelet Transform and Wavelet Based Numerical Methods: an Introduction
Abstract: Wavelet transformation is a new development in the area of applied mathematics. Wavelets are mathematical tools that cut data or functions or operators into different frequency components, and then study each component with a resolution matching to its scale. In this article, we have made a brief discussion on historical development of wavelets, basic definitions, formulations of wave...
متن کامل